Find the exact casting spots for the five original legendary fish
Before upgrading your tackle, make sure your bobber can enter the right water. Each entry below covers an original legendary fish on an unmodded save with ordinary bait; the Extended Family quest uses different fish.
Spring and summer: reach the right depth
For Legend, choose rainy spring weather and reach effective Fishing level 10. Cast into deep Mountain Lake water near the submerged log; the game checks deep water rather than whether the bobber actually touches the wood. Food can raise your effective Fishing level. For Crimsonfish, reach Fishing level 5 in summer and fish from the eastern side of the Beach in sufficiently deep water. Repair the broken wooden bridge with 300 Wood if you cannot reach that side by your ordinary beach route. A long cast from the main dock by Willy is not the same area.
Fall and winter: stand on the named landmark
For Angler, reach Fishing 3 and go to the plank bridge north of JojaMart in fall. For Glacierfish, reach Fishing 6 in winter and use the southern tip of Arrowhead Island in Cindersap Forest. Cast south out from that tip into deep water. Being in the correct region but standing several steps up the island can remove your chance before the minigame even begins. Keep track of whether you see the distinctive legendary fish icon during the fight.
Any season: save a trip for the Sewers
Mutant Carp lives in the Sewers and has no season or time window. You need access to the Sewers, so waiting for rain outside the locked entrance cannot help. Once inside, cast into the green water. On a normal single-player save the original legendary catches are normally once per fish; the later quest relatives are separate entries. If the fish bites and gets away you can keep attempting while the conditions hold. Losing a fight is different from already landing that original fish.